Installing In Design on a new computer and getting all my old work onto it

The info already posted is correct, but something is strange. When I activate a different (third) system, I get a dialog box asking me what device I want to deactivate. Are you sure you are logging in with the same Adobe account?

It's a pretty straightforward process to activate/deactivate devices through your Creative Cloud desktop application.:

1. Open your Adobe Creative Cloud application. When the application window appears, click on the Manage Account link under the account name as shown below.

2. This opens a web page on your default browser. In the pull-down menus at the top of the page, first select the Plans & Pricing pull-down menu, then the Activated Devices command in the pull-down menu, as illustrated below.

This opens a list of your activated devices to use Creative Cloud, as seen in the image below.

Note that in the lead paragraph it says you can only activate two devices. From here it's easy to choose which systems you do/do not want to be running Creative Cloud applications. Eliminate the old computer, make sure the new computer is showing, then return to your new system. You should be able to use your installed Creative Cloud applications in the future.

From this point, it's simply a matter of using your local network or an external drive (a.k.a. Sneakernet) to 1) find all your old work files on your old computer and then 2) copy/transfer those old work files from your old computer to your new one. That's going to be as easy or as hard as your old computer's filing system makes the job. If it's hard to find all the old files on your old computer, this might be the perfect opportunity to set up a better file system that will serve you well on your new one.

Hope this helps,

Randy

Deactivate your subscription on the old computer and a activate it on the new ons. 
you can activate simultaneously on 2 computers. If you cannot activate one more, so if is activated on 2 computers.